Traditional tile tray systems are designed for organizing, displaying, and storing tiles. Such tiles may be counters used in tabletop games, puzzle pieces, or components of educational teaching tools or professional training tools utilizing physical manipulation and arrangement of subcomponents displayed on tiles to create larger designs. For example, individual tiles representing furniture pieces can be arranged on a tile tray representing a room to aid interior design planning. For another example, individual tiles representing atoms and chemical bonds can be arranged on a tile tray to represent molecules. For a further example, individual tiles may display segments of a path, and multiple tiles may be arranged in sequence to create a path extending across the tile tray as part of a game. Tile based systems may be applied to engineering schematics, aerospace, chemistry, medicine, games, computer coding, blue prints, architecture, interior design, fashion, and many other complex areas using physical manipulation and organization of thought patterns (e.g., flow charts), precision drawings, project elements, and visuals. Manipulation of tiles (e.g., adding, removing, moving, rotating or flipping) can be tailored to incorporate the needs of these fields by setting up a dynamic tile system that can rapidly assess several potential possibilities simultaneously, and allow many possible patterns to be created using only a few tiles.
Traditional tile tray systems commonly face two challenges. First, flat tiles placed on a flat tray may be difficult to grasp and lift from the tray. Second, manipulating a tile may result in the manipulated tile contacting an adjacent tile or another tile in proximity to the manipulated tile, moving the other tile and disrupting the arrangement of tiles on the tile tray. It was realized by the inventor that improvements in tile trays are needed to address these challenges and provide other important advantages.